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Simplifying 8x2 + -29x + -1890 = 0 Reorder the terms: -1890 + -29x + 8x2 = 0 Solving -1890 + -29x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -236.25 + -3.625x + x2 = 0 Move the constant term to the right: Add '236.25' to each side of the equation. -236.25 + -3.625x + 236.25 + x2 = 0 + 236.25 Reorder the terms: -236.25 + 236.25 + -3.625x + x2 = 0 + 236.25 Combine like terms: -236.25 + 236.25 = 0.00 0.00 + -3.625x + x2 = 0 + 236.25 -3.625x + x2 = 0 + 236.25 Combine like terms: 0 + 236.25 = 236.25 -3.625x + x2 = 236.25 The x term is -3.625x. Take half its coefficient (-1.8125). Square it (3.28515625) and add it to both sides. Add '3.28515625' to each side of the equation. -3.625x + 3.28515625 + x2 = 236.25 + 3.28515625 Reorder the terms: 3.28515625 + -3.625x + x2 = 236.25 + 3.28515625 Combine like terms: 236.25 + 3.28515625 = 239.53515625 3.28515625 + -3.625x + x2 = 239.53515625 Factor a perfect square on the left side: (x + -1.8125)(x + -1.8125) = 239.53515625 Calculate the square root of the right side: 15.476923346 Break this problem into two subproblems by setting (x + -1.8125) equal to 15.476923346 and -15.476923346.Subproblem 1
x + -1.8125 = 15.476923346 Simplifying x + -1.8125 = 15.476923346 Reorder the terms: -1.8125 + x = 15.476923346 Solving -1.8125 + x = 15.476923346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8125' to each side of the equation. -1.8125 + 1.8125 + x = 15.476923346 + 1.8125 Combine like terms: -1.8125 + 1.8125 = 0.0000 0.0000 + x = 15.476923346 + 1.8125 x = 15.476923346 + 1.8125 Combine like terms: 15.476923346 + 1.8125 = 17.289423346 x = 17.289423346 Simplifying x = 17.289423346Subproblem 2
x + -1.8125 = -15.476923346 Simplifying x + -1.8125 = -15.476923346 Reorder the terms: -1.8125 + x = -15.476923346 Solving -1.8125 + x = -15.476923346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8125' to each side of the equation. -1.8125 + 1.8125 + x = -15.476923346 + 1.8125 Combine like terms: -1.8125 + 1.8125 = 0.0000 0.0000 + x = -15.476923346 + 1.8125 x = -15.476923346 + 1.8125 Combine like terms: -15.476923346 + 1.8125 = -13.664423346 x = -13.664423346 Simplifying x = -13.664423346Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.289423346, -13.664423346}
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